w=cos(theta) + isin(theta) where theta is between 0 and pi.
if complex number w^2 + (5/w) -2 is purely imaginary, show that 2(cos^2)(theta) + 5cos(theta) -3=0.
Hence, find w.
w was found to equal (1/2) + ((sqrt3)/2) i I now know A and B are two points on an Argand diagram representing two distinct non zero complex numbers. z_2 = w(z_1) where w is stated as above.
i found out the following: modulus of (z2/z1) equals 1 Arg (z2/z1) equals pi/3
if o is the origin, what type of triangle is OAB? im guessing the modulus and arg which were asked to be found are revelant somehow. also, am i to assume that A and B are z1 and z2 respectively? otherwise im stuck and the question doesnt clarify. thanks..